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Metric properties of functions defined by partial automata

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Ukrainian Mathematical Journal Aims and scope

We characterize natural categories in which morphisms are defined by partial automata of the following three types: asynchronous automata, window automata, and automata synchronous over finite alphabets. We distinguish subcategories whose morphisms are defined by finite automata.

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References

  1. J.-P. Allouche and J. Shallit, Automatic Sequences: Theory, Applications, Generalizations, Cambridge University Press, Cambridge (2003).

    Book  MATH  Google Scholar 

  2. N. Pytheas Fogg, Substitutions in Dynamics, Arithmetics and Combinatorics, Springer, Berlin (2002).

    Book  MATH  Google Scholar 

  3. D. Perrin and J.-È. Pin, Infinite Words: Automata, Semigroups, Logic and Games, Academic Press, Amsterdam (2004).

    MATH  Google Scholar 

  4. D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge (1995).

    Book  MATH  Google Scholar 

  5. R. I. Grigorchuk, V. V. Nekrashevich, and V. I. Sushchanskii, “Automata, dynamical systems, and groups,” Tr. Mat. Inst. RAN, 231, 134–214 (2000); English translation: Proc. Steklov Inst. Math., 231, No. 4, 128–203 (2000).

    MathSciNet  Google Scholar 

  6. V. Nekrashevych, Self-Similar Groups, American Mathematical Society, Providence, RI (2005).

    MATH  Google Scholar 

  7. R. I. Grigorchuk and V. V. Nekrashevich, “The group of asynchronous automata and rational homeomorphisms of the Cantor set,” Mat. Zametki, 67, No. 5, 680–685 (2001); English translation: Math. Notes, 67, No. 5–6, 577–581 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  8. S. Eilenberg, Automata, Languages and Machines, Academic Press, New York–London (1974).

    MATH  Google Scholar 

  9. G. N. Raney, “Sequential functions,” J. Assoc. Comput. Math., 5, No. 2, 177–180 (1958).

    MathSciNet  MATH  Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 11, pp. 1500–1510, November, 2010.

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Nekrashevich, V.V., Oliinyk, A.S. & Sushchanskii, V.I. Metric properties of functions defined by partial automata. Ukr Math J 62, 1741–1751 (2011). https://doi.org/10.1007/s11253-011-0464-5

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  • DOI: https://doi.org/10.1007/s11253-011-0464-5

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